Saturday, February 05, 2011

Filling the Gap Between ERA and FIP

(Note: This is a heavily sabermetric post rather than a Detroit Tigers post. I'll apply the results to the Tigers in a later post.)

The limitations of ERA are well known in the blogosophere. Two of the biggest issues are:

(1) ERA gives pitchers full responsibility for all hits allowed despite the fact that their control over batted balls is limited. For example, a pitcher with a strong defense behind him will give up less hits (and thus fewer runs) than if he had a poor defense behind him.

(2) ERA gives pitchers full responsibility for sequencing of events. That is, it assumes that they can control when they give up hits and walks. For example, if a pitcher pitches extraordinarily well with runners in scoring position in a given year, he will have a lower ERA than if he had a typical year in those situations.

In reality, pitchers have limited control over both the number of hits they allow and sequencing of events. Thus, Defense Independent Pitching Statistics (DIPS) such as FIP, xFIP, tERA and SIERA have been developed to remove some of the noise of ERA. DIPS are based on things that pitchers do control for the most part - walks, hit batsmen, strikeouts, home runs and types of batted balls (ground balls , fly balls, line drives, pop flies).

Because they are based on things that pitchers essentially control, the DIPS metrics are said to be better measures of true talent than ERA. As a result, they are also better than ERA at predicting future performance. However, they only measure a portion of a pitcher's talent and should be used as complements to ERA rather than as replacements.

While pitchers do have less control over results of batted balls (hits and outs) than they do over walks, strikeouts, homers and ground balls, they do have SOME influence on results of batted balls. Some pitchers are indeed better than others at preventing hits on balls in play. Pitchers also have some control over sequencing of events. Specifically, some pitchers are better than others at pitching with runners on base.

There is a big leap in going from ERA to FIP. Instead of removing hit prevention and sequencing in one step, it might be better to remove one factor at a time. Bill James did that with his Component ERA (ERC). Applying the runs created methodology to pitchers, he determined what a pitcher's ERA should have been based on walks, hit batsmen, strikeouts, homers AND hits allowed. The runs created model is not used much anymore though and linear weights are better, so I wanted to find a similar statistic based on linear weights.

J.T. Jordan at Hardball Times got us part of the way there. He used the Baseball -Reference data on batting against pitchers to calculate wOBA against (or wOBAA). wOBAA for pitchers is calculated the same as wOBA for hitters. The MLB leaders for 2010 are shown in Table 1 below.

Table 1: MLB wOBAA Leaders in 2010

One good feature of wOBA is that it can easily be translated into runs above average (wRAA or RAA). To calculate RAA, subtract league average wOBAA from a player's wOBAA, divide by 1.25 (that number changes from year to year but is usually between 1.15 and 1.25) and multiply by plate appearances. The 2010 leaders are listed in Table 2. Cy Young Award winner Felix Hernandez tops the list at 45 RAA. This means that he saved his team an estimated 45 runs compared to the average pitcher.

Table 2: MLB RAA Leaders in 2010

So, we are almost there. All we need to do is turn RAA into an ERA. Here are the steps:

(1) Calculate MLB average runs scored per nine innings (4.44 in 2010)

(2) Subtract a pitcher' runs above average per nine innings pitched from the league average:
4.44- 9 x RAA/IP

(3) About 93% of runs are earned, so multiply the result in step (2) by .93. The final result is a linear weights component ERA. I'll call it WERC.

Table 3 shows that King Felix led the majors with a 2.60 WERC in 2010.

Table 3: MLB WERC Leaders in 2010

WERC is useful because it gives us an intermediate step between ERA and FIP. For example, Braves right-hander Tim Hudson had a big discrepancy between ERA (2.83) and FIP (4.09)
His WERC was 3.03 which is a lot closer to his ERA. This tells us that a large amount of the difference between FIP and ERA was due to batted balls in play rather than sequencing. We could have figured this out by examining other numbers such as BABIP and LOB%, but it's more convenient to compare three stats on the ERA scale.

Another example is National League Cy Young Award winner Roy Halladay. Halladay's ERA (2.44) was lower than his FIP (3.01). However, his WERC was 3.05 which tells us that the discrepancy was not due to hits allowed but rather sequencing.